Do you still have the tub, and the trip lever, that keeps the water in the tub? If the answer is yes, I'd say a simple first step would be to remove the cover of the trip lever (should just be two screws) and see if the lever is connected to the rod (that pushes/pulls the drain open/shut). If it is connected, it may need to be adjusted.
I would check this before worrying that something large is stuck down there.
Another check to see if the drain is stuck in the closed position (vs. something clogging the pipe) is to pour some water down the overflow opening (again, I'm assuming this is a bathtub). If the water flows down, the drain is stuck in the closed position.